313. Super Ugly Number

Write a program to find the nth super ugly number.

Super ugly numbers are positive numbers whose all prime factors are in the given prime list primes of size k. For example, [1, 2, 4, 7, 8, 13, 14, 16, 19, 26, 28, 32] is the sequence of the first 12 super ugly numbers given primes = [2, 7, 13, 19] of size 4.

Note:
(1) 1 is a super ugly number for any given primes.
(2) The given numbers in primes are in ascending order.
(3) 0 < k ≤ 100, 0 < n ≤ 106, 0 < primes[i] < 1000.
(4) The nth super ugly number is guaranteed to fit in a 32-bit signed integer.

 

求super ugly number。

本题是Ugly Number II的延伸，只是将因数扩展为可变个数。求解方法也大同小异，注意保存每个因数当前所乘的倍数。

代码如下：

int nthSuperUglyNumber(int n, vector<int>& primes)
{
	vector<int> uglyNumbers;
	vector<int> coef(primes.size(), 0);
	uglyNumbers.push_back(1);
	int ugly = 1;
	while ((int)uglyNumbers.size() < n)
	{
		vector<int> vals;
		for (int i = 0; i < (int)primes.size(); i++)
			vals.push_back(uglyNumbers.at(coef[i])*primes[i]);
		ugly = vals[0];
		for (int val : vals)
			if (val < ugly)
				ugly = val;
		uglyNumbers.push_back(ugly);
		for (int i = 0; i < (int)coef.size(); i++)
			if (vals[i] == ugly)
				coef[i]++;
	}
	return ugly;
}